Decision feedback equalizers have been used to recover digital signals after transmission over narrow band channels. If the intersymbol interference caused by such a channel is represented by its impulse response, this impulse response includes a positive maxima, called the "cursor" and representing the preferred data signal, and an extended region extending on both sides of the maxima. Precursor intersymbol interference signals (preceding the cursor) are typically canceled by an in-line filter in the received signal path while the post cursor intersymbol interference is canceled by an adaptive feedback filter. It has been proposed in the copending application of the present applicants, Ser. No. 392,773, filed Aug. 11, 1989, now matured into U.S. Pat. No. 5,031,194, issued Jul. 9, 1991, and assigned to applicants' assignee, to break the post-cursor region of the impulse response into two contiguous regions, a rapidly varying region compensated by a finite impulse response (FIR) and a slowly changing tail region compensated by an infinite impulse response (IIR), or pole-zero filter. The FIR filter includes a moderate number of taps since the intersymbol interference due to the rapidly varying region is limited. The IIR filter, although canceling a much longer region, has only a few taps because the tail of the impulse response is accurately modeled by a two-pole filter section. Both the FIR filter and the IIR filter are adapted using the equation error algorithm. It is to be noted that the equation error minimized in the abovenoted patent application is not the true performance criterion. The configuration described therein trades residual intersymbol interference, caused by a biased channel estimate, for noise enhancement, caused by a longer prefilter.
J. J. Shynk in "Adaptive IIR Filtering," IEEE ASSP Magazine, Vol. 6, No. 2, pages 4-21, April 1989, and C. R. Johnson, in "Adaptive IIR Filtering: Current Results and Open Issues," IEEE Transactions on Information Theory, Vol. IT-30, No. 2, pages 237-250, March 1984, have described the use a gradient algorithm to adapt IIR filters in other applications. Unfortunately, in this algorithm, the coefficients of the filters are strongly interdependent, resulting in very slow convergence.
It has also been proposed to use an identification algorithm for adapting infinite impulse response filters in another context by K. Steiglitz and L. McBride in "A Technique for the Identification of Linear Systems," IEEE Transactions on Automatic Control, Vol. AC-10, pages 461-464, October, 1965. Unfortunately, this algorithm is designed for use with stored blocks of data and is not useful for serial sequential data as is found in subscriber loop data transmission. Moreover, this algorithm is computationally expensive.
A sequential version of the identification algorithm of the Steiglitz and McBride article is proposed by H. Fan and W. K. Jenkins in "A New Adaptive IIR Filter," IEEE Transactions on Circuits and Systems, Vol. CAS-33, No. 10, pages 939-947, October, 1986. Unfortunately this sequential identification algorithm converges no more quickly than the gradient algorithm described above.